WASHINGTON — The House impeachment managers opened their prosecution of Donald J. Trump on Wednesday with a meticulous account of his campaign to overturn the election and goad supporters to join him, bringing its most violent spasms to life with never-before-seen security footage from the Jan. 6 Capitol riot.

Filling the Senate chamber with the profane screams of the attackers, images of police officers being brutalized, and near-miss moments in which Vice President Mike Pence and lawmakers came steps away from confronting a mob hunting them down, the prosecutors made an emotional case that Mr. Trump’s election lies had directly endangered the heart of American democracy.

They played frantic police radio calls warning that “we’ve lost the line,” body camera footage showing an officer pummeled with poles and fists on the West Front of the Capitol, and silent security tape from inside showing Mr. Pence, his family and members of the House and Senate racing to evacuate as the mob closed in, chanting: “Hang Mike Pence! Hang Mike Pence!”

All of it, the nine Democratic managers said, was the foreseeable and intended outcome of Mr. Trump’s desperate attempts to cling to the presidency. Reaching back as far as last summer, they traced how he spent months cultivating not only the “big lie” that the election was “rigged” against him, but stoking the rage of a throng of supporters who made it clear that they would do anything — including resorting to violence — to help him.

The managers argued that it warranted that the Senate break with two centuries of history to make Mr. Trump the first former president to be convicted in an impeachment trial and disqualified from future office on a single count of “incitement of insurrection.”

“Donald Trump surrendered his role as commander in chief and became the inciter in chief of a dangerous insurrection,” Representative Jamie Raskin, Democrat of Maryland and the lead manager, told the senators. They watched the footage in silence in the same spots where they had been when the mob breached the building last month.

“He told them to ‘fight like hell,’” Mr. Raskin added, quoting the speech that Mr. Trump gave supporters as the onslaught was unfolding, “and they brought us hell on that day.”

Though the House managers used extensive video evidence of the Jan. 6 riot to punctuate their case, they spent just as much time placing the event in the context of Mr. Trump’s broader effort to falsely claim the election had been stolen from him, portraying him as a president increasingly desperate to invalidate the results.

“With his back against the wall, when all else has failed, he turns back to his supporters — who he’d already spent months telling that the election was stolen — and he amplified it further,” said Representative Joe Neguse, Democrat of Colorado.

After dozens of frivolous lawsuits failed, the managers said, Mr. Trump began pressuring officials in key battleground states like Michigan, Pennsylvania and Georgia to overturn his losses there. When that failed, he tried the Justice Department, then publicly attempted to shame Republican members of Congress into helping him. Finally, he insisted that Mr. Pence assume nonexistent powers to unilaterally overturn their loss on Jan. 6, when the vice president would oversee the counting of the electoral votes in Congress.

“Let me be clear: The president was not just coming for one or two people, or Democrats like me,” said Representative Ted Lieu of California, looking out at senators. “He was coming for you.”

At the same time, the managers argued, the president was knowingly encouraging his followers to take matters into their own hands. When an armada of his supporters tried to run a Biden campaign bus off the highway in October, Mr. Trump cheered them on Twitter. He began adopting increasingly violent language, they noted, and did nothing to denounce armed mobs cropping up in his name in cities around the country. Instead, he repeatedly invited them to Washington on Jan. 6 to rally to “stop the steal” as Congress met to formalize President-elect Joseph R. Biden Jr.’s victory.

“When he saw firsthand the violence that his conduct was creating, he didn’t stop it,” Mr. Neguse said. “He didn’t condemn the violence. He incited it further and he got more specific. He didn’t just tell them to fight like hell. He told them how, where and when.”

At times, the presentation, delivered by a group of Democrats with extensive courtroom experience, resembled a criminal prosecution — only in this case, the jury was made up of senators who were also witnesses struggling as they relived in graphic detail the trauma of that day.

Delegate Stacey Plaskett of the U.S. Virgin Islands guided them through much of the video, including scenes of rioters inside the Capitol tauntingly calling for Speaker Nancy Pelosi and flooding into her office just after aides had raced to barricade themselves in a conference room and hid under a table.

“Nancy! Oh, Nancy! Where are you, Nancy?” one of the invaders could be heard shouting in a singsong voice.

“That was a mob sent by the president of the United States to stop the certification of an election,” Ms. Plaskett said. “President Trump put a target on their backs, and his mob broke into the Capitol to hunt them down.”

Glued to their desks, some senators recoiled or averted their eyes from the hours of footage, including of their own evacuation as the mob closed in just down a corridor.

“It tears at your heart and brings tears to your eyes,” said Senator Mitt Romney, Republican of Utah, who could be seen in one of the videos racing back toward the Senate for safety. “That was overwhelmingly distressing and emotional.”

Senator John Thune of South Dakota, the No. 2 Senate Republican, conceded that the managers had “done a good job connecting the dots” and recreating a “harsh reminder of what happens when you let something like that get out of hand.” Five people died in connection to the mayhem, including a Capitol Police officer, and more than 100 were injured.

But for all of the power of their case, the managers’ task remained an exceedingly steep one, and it was unclear if they had made any headway. Senators voted narrowly to proceed with the trial on Tuesday, but only six Republicans joined Democrats in deeming it constitutional to judge an official no longer in office, foreshadowing Mr. Trump’s likely acquittal.

Many of the same Republicans who had been hostile to hearing the case did not dispute on Wednesday the horror of the attack, but they suggested it was the rioters, not the former president who retains heavy sway over their party, who are culpable.

“Today’s presentation was powerful and emotional, reliving a terrorist attack on our nation’s capital,” said Senator Ted Cruz, Republican of Texas. “But there was very little said about how specific conduct of the president satisfies the legal standard.”

Short of persuading 34 Republicans to join Democrats to achieve the two-thirds majority necessary to convict, the Democratic managers directed their arguments at the American public and at history in an attempt to bury Mr. Trump’s popular appeal and lay down a clear marker for future presidents.

The trial was proceeding at a blistering pace. Prosecutors were expected to take several more hours on Thursday before Mr. Trump’s lawyers will have two days to mount a defense. The Senate could render a verdict as soon as the weekend.

Mr. Trump’s lawyers, who made a much-criticized debut on Tuesday, are expected to assert that the former president was not trying to incite violence or interfere with the electoral process. Rather, they will argue, he merely wanted to urge his supporters to demand general election security reforms, an argument that requires ignoring much of the evidentiary record.

Though they have sought not to repeat Mr. Trump’s outlandish claims that the election was “stolen” from him, the lawyers will also insist they amount to constitutionally protected free speech for which the Senate cannot punish him.

The House managers, though, argued that Mr. Trump clearly incited the attack, thus violating his oath of office to protect the Constitution.

Prosecutors walked senators through his speech just before the mob closed in, playing again and again clips of him urging the thousands on hand to “fight like hell” alongside others, shot from the crowd, featuring a drastic response from the audience: “Take the Capitol.”

“This violent attack was not planned in secret,” Ms. Plaskett said. “The insurgents believed they were doing the duty of their president — they were taking his orders.”

To bolster their analysis, the managers turned to an unlikely group: the hundreds of people already charged with executing the riot who in interviews and court records leave little doubt that they believed they were delivering to Mr. Trump what he asked for.

But it was all a prelude to a vivid recreation of the attack itself meant to drive home the enormity of what the managers said Mr. Trump had unleashed. Mindful that individual lawmakers still had only a limited view of the day, they used a computer generated model of the Capitol to show in precise detail the mob’s movements over time relative to members of Congress.

In one jarring scene, Senator Chuck Schumer, Democrat of New York and the minority leader at the time, was shown literally running with a security detail through the basement of the Senate in search of safety. Representative Eric Swalwell of California, another of the impeachment managers, told senators he had counted 58 steps between where senators could be seen scurrying toward a secure location and where armed extremists were massing.

Instead of intervening to help as the Capitol fell, the managers asserted that Mr. Trump simply stood back and watched in a “dereliction of duty” as the second and third in line to the presidency were put in peril. Citing news reports and accounts from Republican senators themselves who contacted the White House desperate for the president to call off the attack or send in security reinforcements, the managers said the evidence suggested Mr. Trump refused because he was “delighted” with what he saw unfolding.

“When the violence started, he never once said the one thing everyone around him was begging him to say,” Representative Joaquin Castro of Texas said. “‘Stop the attack.’”

Emily Cochrane contributed reporting.